COORDINATIONNUMBER

This is part of the symfunc module | |

It is only available if you configure PLUMED with ./configure –enable-modules=symfunc . Furthermore, this feature is still being developed so take care when using it and report any problems on the mailing list. |

Calculate the coordination numbers of atoms so that you can then calculate functions of the distribution of coordination numbers such as the minimum, the number less than a certain quantity and so on.

So that the calculated coordination numbers have continuous derivatives the following function is used:

\[ s = \frac{ 1 - \left(\frac{r-d_0}{r_0}\right)^n } { 1 - \left(\frac{r-d_0}{r_0}\right)^m } \]

If R_POWER is set, this will use the product of pairwise distance raised to the R_POWER with the coordination number function defined above. This was used in White and Voth [114] as a way of indirectly biasing radial distribution functions. Note that in that reference this function is referred to as moments of coordination number, but here we call them powers to distinguish from the existing MOMENTS keyword of Multicolvars.

- Examples

The following input tells plumed to calculate the coordination numbers of atoms 1-100 with themselves. The minimum coordination number is then calculated.

Click on the labels of the actions for more information on what each action computes

COORDINATIONNUMBERSPECIES=1-100this keyword is used for colvars such as coordination number.R_0=1.0could not find this keywordMIN={BETA=0.1} The COORDINATIONNUMBER action with labelcalculate the minimum value.

@0_grp:GROUPATOMS=1-100 The GROUP action with labelthe numerical indexes for the set of atoms in the group.@0_grpdefines a group of atoms so that they can be referred to later in the input@0_mat:CONTACT_MATRIXGROUP=1-100specifies the list of atoms that should be assumed indistinguishable.R_0=1.0could not find this keywordD_0=0.0could not find this keywordNN=6compulsory keyword ( default=6 )The n parameter of the switching functionMM=0 The CONTACT_MATRIX action with labelcompulsory keyword ( default=0 )The m parameter of the switching function; 0 implies 2*NN@0_matcalculates a single scalar value@0_ones:ONESSIZE=100 The ONES action with labelcompulsory keywordthe number of ones that you would like to create@0_onescalculates a single scalar value@0:MATRIX_VECTOR_PRODUCTARG=the input for this action is the scalar output from one or more other actions.@0_mat,@0_onesThe MATRIX_VECTOR_PRODUCT action with label@0calculates a single scalar value@0_caverage:MEANARG=the input to this function.@0PERIODIC=NO The MEAN action with labelcompulsory keywordif the output of your function is periodic then you should specify the periodicity of the function.@0_caveragecalculates a single scalar value@0_me_min:CUSTOMARG=the input to this function.@0FUNC=exp(0.1/x)compulsory keywordthe function you wish to evaluatePERIODIC=NO The CUSTOM action with labelcompulsory keywordif the output of your function is periodic then you should specify the periodicity of the function.@0_me_mincalculates a single scalar value@0_mec_min:SUMARG=the input to this function.@0_me_minPERIODIC=NO The SUM action with labelcompulsory keywordif the output of your function is periodic then you should specify the periodicity of the function.@0_mec_mincalculates a single scalar value@0_min:CUSTOMARG=the input to this function.@0_mec_minFUNC=0.1/log(x)compulsory keywordthe function you wish to evaluatecompulsory keywordif the output of your function is periodic then you should specify the periodicity of the function.@0_mincalculates a single scalar value

The following input tells plumed to calculate how many atoms from 1-100 are within 3.0 of each of the atoms from 101-110. In the first 101 is the central atom, in the second 102 is the central atom and so on. The number of coordination numbers more than 6 is then computed.

Click on the labels of the actions for more information on what each action computes

COORDINATIONNUMBERSPECIESA=101-110this keyword is used for colvars such as the coordination number.SPECIESB=1-100this keyword is used for colvars such as the coordination number.R_0=3.0could not find this keywordMORE_THAN={RATIONAL R_0=6.0 NN=6 MM=12 D_0=0} The COORDINATIONNUMBER action with labelcalculate the number of variables that are more than a certain target value.

@0_grp:GROUPATOMS=101-110 The GROUP action with labelthe numerical indexes for the set of atoms in the group.@0_grpdefines a group of atoms so that they can be referred to later in the input@0_mat:CONTACT_MATRIXGROUPA=101-110.GROUPB=1-100.R_0=3.0could not find this keywordD_0=0.0could not find this keywordNN=6compulsory keyword ( default=6 )The n parameter of the switching functionMM=0 The CONTACT_MATRIX action with labelcompulsory keyword ( default=0 )The m parameter of the switching function; 0 implies 2*NN@0_matcalculates a single scalar value@0_ones:ONESSIZE=100 The ONES action with labelcompulsory keywordthe number of ones that you would like to create@0_onescalculates a single scalar value@0:MATRIX_VECTOR_PRODUCTARG=the input for this action is the scalar output from one or more other actions.@0_mat,@0_onesThe MATRIX_VECTOR_PRODUCT action with label@0calculates a single scalar value@0_caverage:MEANARG=the input to this function.@0compulsory keywordif the output of your function is periodic then you should specify the periodicity of the function.@0_caveragecalculates a single scalar value@0_mt:MORE_THANARG=the input to this function.@0SWITCH=RATIONAL,R_0=6.0,NN=6,MM=12,D_0=0 The MORE_THAN action with labelThis keyword is used if you want to employ an alternative to the continuous swiching function defined above.@0_mtThe following input tells plumed to calculate the mean coordination number of all atoms with themselves and its powers. An explicit cutoff is set for each of 8.

Click on the labels of the actions for more information on what each action computescn0:COORDINATIONNUMBERSPECIES=1-10this keyword is used for colvars such as coordination number.SWITCH={RATIONAL R_0=1.0 D_MAX=8}the switching function that it used in the construction of the contact matrixMEANYou cannot view the components that are calculated by each action for this input file. Sorry( default=off ) calculate the mean of all the quantities.cn1:COORDINATIONNUMBERSPECIES=1-10this keyword is used for colvars such as coordination number.SWITCH={RATIONAL R_0=1.0 D_MAX=8}the switching function that it used in the construction of the contact matrixR_POWER=1compulsory keywordthe power to which you want to raise the distanceMEANYou cannot view the components that are calculated by each action for this input file. Sorry( default=off ) calculate the mean of all the quantities.cn2:COORDINATIONNUMBERSPECIES=1-10this keyword is used for colvars such as coordination number.SWITCH={RATIONAL R_0=1.0 D_MAX=8}the switching function that it used in the construction of the contact matrixR_POWER=2compulsory keywordthe power to which you want to raise the distanceMEANYou cannot view the components that are calculated by each action for this input file. Sorry PRINT( default=off ) calculate the mean of all the quantities.ARG=the input for this action is the scalar output from one or more other actions.cn0.mean,cn1.mean,cn2.meanSTRIDE=1compulsory keyword ( default=1 )the frequency with which the quantities of interest should be outputFILE=cn_out You cannot view the components that are calculated by each action for this input file. Sorrythe name of the file on which to output these quantities

- Glossary of keywords and components

- Description of components

QuantityKeywordDescriptionlessthanLESS_THANthe number of colvars that have a value less than a threshold morethanMORE_THANthe number of colvars that have a value more than a threshold altminALT_MINthe minimum value of the cv minMINthe minimum colvar maxMAXthe maximum colvar betweenBETWEENthe number of colvars that have a value that lies in a particular interval highestHIGHESTthe largest of the colvars lowestLOWESTthe smallest of the colvars sumSUMthe sum of the colvars meanMEANthe mean of the colvars momentMOMENTSthe moments of the distribution

- The atoms involved can be specified using

SPECIESthis keyword is used for colvars such as coordination number. In that context it specifies that plumed should calculate one coordination number for each of the atoms specified. Each of these coordination numbers specifies how many of the other specified atoms are within a certain cutoff of the central atom. You can specify the atoms here as another multicolvar action or using a MultiColvarFilter or ActionVolume action. When you do so the quantity is calculated for those atoms specified in the previous multicolvar. This is useful if you would like to calculate the Steinhardt parameter for those atoms that have a coordination number more than four for example

- Or alternatively by using

SPECIESAthis keyword is used for colvars such as the coordination number. In that context it species that plumed should calculate one coordination number for each of the atoms specified in SPECIESA. Each of these cooordination numbers specifies how many of the atoms specifies using SPECIESB is within the specified cutoff. As with the species keyword the input can also be specified using the label of another multicolvar SPECIESBthis keyword is used for colvars such as the coordination number. It must appear with SPECIESA. For a full explanation see the documentation for that keyword

- Compulsory keywords

NN( default=6 ) The n parameter of the switching function MM( default=0 ) The m parameter of the switching function; 0 implies 2*NN D_0( default=0.0 ) The d_0 parameter of the switching function R_0The r_0 parameter of the switching function R_POWERthe power to which you want to raise the distance

- Options

HIGHEST( default=off ) this flag allows you to recover the highest of these variables. LOWEST( default=off ) this flag allows you to recover the lowest of these variables. SUM( default=off ) calculate the sum of all the quantities. MEAN( default=off ) calculate the mean of all the quantities. LOWMEM( default=off ) this flag does nothing and is present only to ensure back-compatibility

SWITCHthe switching function that it used in the construction of the contact matrix LESS_THANcalculate the number of variables that are less than a certain target value. This quantity is calculated using \(\sum_i \sigma(s_i)\), where \(\sigma(s)\) is a switchingfunction.. You can use multiple instances of this keyword i.e. LESS_THAN1, LESS_THAN2, LESS_THAN3... MORE_THANcalculate the number of variables that are more than a certain target value. This quantity is calculated using \(\sum_i 1 - \sigma(s_i)\), where \(\sigma(s)\) is a switchingfunction.. You can use multiple instances of this keyword i.e. MORE_THAN1, MORE_THAN2, MORE_THAN3... ALT_MINcalculate the minimum value. To make this quantity continuous the minimum is calculated using \( \textrm{min} = -\frac{1}{\beta} \log \sum_i \exp\left( -\beta s_i \right) \) The value of \(\beta\) in this function is specified using (BETA= \(\beta\)). MINcalculate the minimum value. To make this quantity continuous the minimum is calculated using \( \textrm{min} = \frac{\beta}{ \log \sum_i \exp\left( \frac{\beta}{s_i} \right) } \) The value of \(\beta\) in this function is specified using (BETA= \(\beta\)) MAXcalculate the maximum value. To make this quantity continuous the maximum is calculated using \( \textrm{max} = \beta \log \sum_i \exp\left( \frac{s_i}{\beta}\right) \) The value of \(\beta\) in this function is specified using (BETA= \(\beta\)) BETWEENcalculate the number of values that are within a certain range. These quantities are calculated using kernel density estimation as described on histogrambead.. You can use multiple instances of this keyword i.e. BETWEEN1, BETWEEN2, BETWEEN3... HISTOGRAMcalculate a discretized histogram of the distribution of values. This shortcut allows you to calculates NBIN quantites like BETWEEN. MOMENTSthe list of moments that you would like to calculate